Nick Kristof has one answer: Focus on the individuals in the story, leaving the aid bureaucracies just outside the frame. Make readers care about places and people they will probably never see by bringing them stories of hope and inspiration: the American woman who leaves behind her family to help rape survivors in the Congo; the orphan boy in Zimbabwe who dreams of and gets a bicycle.
Philip Gourevitch, writing in the New Yorker this week, has another:

…Surely at least we who work in journalism can do a public service by treating humanitarianism the same way we treat other powerful public interests that shape our world…Why should our coverage of them look so much like their own self-representation in fund-raising appeals? Why should we (as many photojournalists and print reporters do) work for humanitarian agencies between journalism jobs, helping them with their official reports and institutional appeals, in a way that we would never consider doing for corporations, political parties, or government agencies? Why should we not regard them as interested parties in the public realms in which they operate, as giant bureaucracies, as public trusts, with long records of getting it wrong with catastrophic consequences, as well as getting it right?

…[H]umanitarianism is an industry. So we should examine it and hold it to account as such. To treat humanitarian or human-rights organizations with automatic deference, as if they were disinterested higher authorities rather than activists and lobbyists with political and institutional interests and biases, and with uneven histories of reliability or success, is to do ourselves, and them, a disservice. That does not mean—as the many books I reviewed, and many more still, make clear—taking a hostile stance toward N.G.O.s. It simply means not accepting their hostility to critical scrutiny. It means not letting them claim to do our work for us. It means insisting on asking the questions for which they may have no good answers.